In my textbooks solution it says
getsuyoubi ha itsumo ani to isshoni tabemasu
I thought it would be
Thank you in advance
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So, first of all, the sentence （私は）月曜日にいつも兄と一緒に食べます。 is grammatically totally fine and would be comprehended in the context you give. This would probably best structurally translate as
"I usually/always eat with my brother on Mondays"
However, partly because Japanese is a pronoun-drop language, and partly because of the situation -- where the speaker has been asked about going for pizza (presumably on a Monday) -- 月曜日はいつも兄と一緒に食べます might well be preferable here.
The reason for that is that he's focusing on the concept of Monday, so it makes sense to make it the topic/discourse of the conversation. In comparison to the above sentence, you'll thus get a structural translation of something closer to
"On Mondays, I usually/always eat with my brother".
Using は thus makes it a bit clearer that it's the pizza invitation being on a Monday that is the issue as to why he can't go, which is appropriate for this context.
Hope that helps.